This topic is really fun and useful! We are going to explore the graphs of quadratic functions. These functions all have the same basic U-shape graph called a parabola. A parabola's equation takes on two forms: the standard form of a parabola y=a(x-h)2+k and the general form of a parabola y=ax2+bx+c. This lesson covers analyzing these equations algebraically and producing the graphs manually.
Be sure that you can find all the information (vertex, intercepts, etc.) no matter which form of the equation you are given.

Objectives

By the end of this topic you should know and be prepared to be tested on:

12.1.1 Know the graph of the basic parabola y=x2 including specific points that lie on it

12.1.2 Recognize and be able to perform reflections (flips across the x-axis), stretches, vertical shifts (up or down), and horizontal shifts (left or right)

12.1.3 Know what values in the parabola's equation controls the above features (shifts, etc.) of the graph

12.1.4 Given either form of a parabola, know that the a-value gives you information about which way the parabola opens and how wide/narrow that opening is.

12.1.5 Given the standard form of a parabola, be able to identify the a, h, and k-values and know that the k-term is the shift up/down, the h-term is the shift left/right, and the vertex is the point (h,k).

12.1.6 Given the general form of a parabola, be able to identify the a, b, and c-values and know the vertex is the point (-b/(2a),f(-b/(2a))).

12.1.7 Given either form of a parabola, know how to algebraically find the y-intercept (by letting x=0) and the x-intercepts (by letting y=0 and solving for x using factoring, the root method, CTS, or the quadratic formula as needed)

12.1.8 Pull all the known information about a parabola together and manually produce its graph